In sports betting there is a well-documented anomaly called the Favorite Longshot Bias (FLB). In the majority of betting markets, the implied probabilities, derived from betting odds, are too high for underdogs. Implied probabilities are calculated by one divided by the decimal odds. Let's say Nadal plays against Federer. Decimal betting odds are 2 for both players. That means that the implied probability of each player winning is 1/2=0.5=50%. If Nadal were to play against the very strong, up and coming, Kruxdelux odds might be 100 for Kruxi (1% implied probability) and 1.01 (99% implied probability) for Nadal. But Kruxi really isn’t that good of a player, sure back in Schwarzenbergclub 2006 summer camp he made second place, but that’s about it. Deluxi will not win 1/100 times but 1/1000 times. And Nadal will win in 999/1000 cases rather than just in 990/1000 cases. That’s a huge difference. This means that betting on Kruxi at odds 100 is a really bad idea and betting on Nadal is a really good idea.
This scenario is commonplace in the betting market. Numerous papers have compared implied probabilities of betting odds with event outcomes and found that underdogs are over-priced and (in some extreme cases) favorites are under-priced. There are four explanations to why this could be the case:
1. Behavioral: From behavioral literature, we get evidence that people love betting on stuff that could yield high profits, regardless of the expected value (probability*outcome). People play the lottery although the expected value is less than 1. The same rationale is used for this explanation. Bookmakers know that punters love betting on the underdog and thus the price of betting on it is high (the odds are too low). On the other hand, punters are not too eager to get 1.01 on their 1 Euro bet and thus are less likely to bet on it, the price of it is thus low (and odds are too high). Here the thrill of possibly winning big might make up for negative expected value. But since we know I am not a huge fan of behavioral economics lets have a look at some other explanations.
2. A lovely classical explanation evolves around bookmaker’s hedging against insiders and betting fraud. Match-fixing is not uncommon. Here people can win big if they bribe both players and make sure the underdog wins, while also betting on the underdog. To hedge against this scenario, bookmakers always tend to give slightly lower odds to longshots. This hedges against fraud and match-fixing. I tried to model this in an experimental setting.
3. Another supply-side theory predicts that odds reflect cost of information acquisition. In scenario its not necessarily the longshot that is overvalued, but the player of which lesser is known. But in most cases, the longshot is also the less known player. In this case, costs of acquiring information and uncertainty lead to worse odds than the true probabilities predict. Again, I tried to model that with tennis players age (as a proxi for available information) in an econometric model.
4. Lastly, collusion may be the reason for this anomaly. Academic papers found that the FLB is extremely harsh in only certain matches, at certain times, with certain conditions, indicating that there might be collusion among bookmakers. To maximize profit, they decide to give extremely bad odds to the underdog at certain events only. The evidence for that is pretty good at low stake horse and greyhound races.
In general, you shouldn't bet. Bookmakers take a high rake and overround you will not find odds of 2 and 2 in the above-mentioned case of Federer vs Nadal. Odds are more likely to be 1.8 and 1.8, thus you losing in the long-run. If you find yourself in the situation where you “have to bet”, when going to Ascot with your friends or pre-match betting on football game attended with family, bet on the favorite. In the long run, you will lose less.
To read more on this topic you can find my St. Andrews Msc dissertation here.
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